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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 32192k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32192.n1 | 32192k1 | \([0, -1, 0, 319, 193]\) | \(13651919/8048\) | \(-2109734912\) | \([]\) | \(18432\) | \(0.47852\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32192k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 32192k do not have complex multiplication.Modular form 32192.2.a.k
sage: E.q_eigenform(10)